Mixed integer quadratic optimization formulations for eliminating multicollinearity based on variance inflation factor
Mixed integer quadratic optimization formulations for eliminating multicollinearity based on variance inflation factor
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DOI：
10.1007/s10898-018-0713-3
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发表时间：
2018-10
影响因子：
1.8
通讯作者：
Ryuta Tamura;Ken Kobayashi;Yuichi Takano;Ryuhei Miyashiro;K. Nakata;Tomomi Matsui
中科院分区：
文献类型：
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作者：
Ryuta Tamura;Ken Kobayashi;Yuichi Takano;Ryuhei Miyashiro;K. Nakata;Tomomi Matsui
当多元线性回归模型的某些解释变量高度相关时，存在多重共线性。解释变量之间的高度相关性降低了分析的可靠性。为了消除线性回归模型中的多重共线性，我们考虑如何通过方差膨胀因子（VIF）选择显著变量的子集，这是检测多重共线性时最常用的指标。特别是，我们采用混合整数优化（MIO）的方法来选择子集。MIO方法于20世纪70年代提出，最近由于算法和硬件的进步而重新受到关注。然而，没有现有的研究已经开发出一个计算上易于处理的MIO配方消除多重共线性的基础上的VIF。在本文中，我们提出了混合整数二次优化（MIQO）配方选择最好的解释变量的子集上界的VIF选定的变量。我们的两个MIQO公式是基于VIF的两个等价定义。计算结果表明，我们的MIQO配方与传统的局部搜索算法和基于MIO的切割平面算法的有效性。
Multicollinearity exists when some explanatory variables of a multiple linear regression model are highly correlated. High correlation among explanatory variables reduces the reliability of the analysis. To eliminate multicollinearity from a linear regression model, we consider how to select a subset of significant variables by means of the variance inflation factor (VIF), which is the most common indicator used in detecting multicollinearity. In particular, we adopt the mixed integer optimization (MIO) approach to subset selection. The MIO approach was proposed in the 1970s, and recently it has received renewed attention due to advances in algorithms and hardware. However, none of the existing studies have developed a computationally tractable MIO formulation for eliminating multicollinearity on the basis of VIF. In this paper, we propose mixed integer quadratic optimization (MIQO) formulations for selecting the best subset of explanatory variables subject to the upper bounds on the VIFs of selected variables. Our two MIQO formulations are based on the two equivalent definitions of VIF. Computational results illustrate the effectiveness of our MIQO formulations by comparison with conventional local search algorithms and MIO-based cutting plane algorithms.